Question

G and H are mutually exclusive events. P(G)=0.5 P(H)=0.3. a. Explain why the following statement MUST...

G and H are mutually exclusive events. P(G)=0.5 P(H)=0.3. a. Explain why the following statement MUST be false: P(H|G)=0.4. b. Find P(H OR G). c. Are G and H independent or dependent events? Explain in a complete sentence.

Solution:
We are given that: G and H are mutually exclusive events.

Thus

and we are also given that: P(G)=0.5 P(H)=0.3.

Part a) Explain why the following statement MUST be false: P(H|G)=0.4.

Since , P( H | G) becomes 0.

Hence given statement P(H|G)=0.4 must be false.

Part b) Find P(H OR G).

Since G and H are mutually exlcusive events,

P( H or G) = P(H) + P(G)

P( H or G) = 0.3 + 0.5

P( H or G) = 0.8

Part c) Are G and H independent or dependent events?

Events are independent if and only if:

We have

and

P(G) X P(H) = 0.5 X 0.3

P(G) X P(H) = 0.15

Thus we get:

Hence events G and H are not independent,

that is: events G and H are dependent events.

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